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.\"     from: @(#)hypot.3	6.7 (Berkeley) 5/6/91
.\"
.Dd $Mdocdate: January 15 2015 $
.Dt HYPOT 3
.Os
.Sh NAME
.Nm hypot ,
.Nm hypotf ,
.Nm hypotl ,
.Nm cabs ,
.Nm cabsf ,
.Nm cabsl
.Nd Euclidean distance and complex absolute value functions
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn hypot "double x" "double y"
.Ft float
.Fn hypotf "float x" "float y"
.Ft long double
.Fn hypotl "long double x" "long double y"
.In complex.h
.Ft double
.Fn cabs "double complex z"
.Ft float
.Fn cabsf "float complex z"
.Ft long double
.Fn cabsl "long double complex z"
.Sh DESCRIPTION
The
.Fn hypot ,
.Fn hypotf
and
.Fn hypotl
functions
compute the
sqrt(x*x+y*y)
in such a way that underflow will not happen, and overflow
occurs only if the final result deserves it.
.Pp
.Fn hypot "\*(If" "v"
=
.Fn hypot "v" "\*(If"
= +\*(If for all
.Ar v ,
including \*(Na.
.Pp
The
.Fn cabs ,
.Fn cabsf
and
.Fn cabsl
functions return the absolute value of the complex number
.Fa z .
.Sh ERRORS (due to Roundoff, etc.)
Below 0.97
.Em ulps .
Consequently
.Fn hypot "5.0" "12.0"
= 13.0
exactly;
in general, hypot and cabs return an integer whenever an
integer might be expected.
.Sh NOTES
As might be expected,
.Fn hypot "v" "\*(Na"
and
.Fn hypot "\*(Na" "v"
are \*(Na for all
.Em finite
.Ar v ;
with
.Dq reserved operand
in place of "\*(Na", the same is true on a VAX.
But programmers on machines other than a VAX (it has no \*(If)
might be surprised at first to discover that
.Fn hypot "\(+-\*(If" "\*(Na"
= +\*(If.
This is intentional; it happens because
.Fn hypot "\*(If" "v"
= +\*(If
for
.Em all
.Ar v ,
finite or infinite.
Hence
.Fn hypot "\*(If" "v"
is independent of
.Ar v .
Unlike the reserved operand fault on a VAX,
the IEEE \*(Na is designed to disappear
when it turns out to be irrelevant, as it does in
.Fn hypot "\*(If" "\*(Na" .
.Sh SEE ALSO
.Xr sqrt 3
.Sh HISTORY
A
.Fn hypot
function first appeared in
.At v3 ,
and
.Fn cabs
in
.At v7 .
